https://r2.erweima.ai/mathbot/image/1725324500209qfzdq1pc.jpg

Utilice la calculadora y encuentre el valor aproximado de las siguientes expresiones: 

The image contains mathematical expressions that require evaluation using a calculator. I'll read the expressions from the image and compute their approximate values.

### Expressions to Evaluate

1. \(\sqrt[3]{-97}\)
2. \(-97^{\frac{1}{3}}\)
3. \(\sqrt[3]{-5^3}\)

Now, I will evaluate these expressions:

1. \(\sqrt[3]{-97}\): The cube root of \(-97\).
2. \(-97^{\frac{1}{3}}\): This is equivalent to the first expression since it's another way of writing the cube root.
3. \(\sqrt[3]{-5^3}\): The cube root of \(-5^3\).

### Calculations

1. \(\sqrt[3]{-97} \approx -4.6348\)
2. \(-97^{\frac{1}{3}} \approx -4.6348\) (Same as the first expression)
3. \(\sqrt[3]{-5^3} = -5\)

These values are approximate for the first two expressions, and exact for the third one.

Would you like more details or have any questions? Here are five related questions that could expand your understanding:

1. How do you evaluate the cube root of a negative number?
2. What is the difference between a square root and a cube root?
3. How can the cube root be represented differently in various mathematical notations?
4. What are the properties of cube roots in terms of their behavior with negative numbers?
5. How would you approximate the value of cube roots without a calculator?

**Tip:** Cube roots can be evaluated even for negative numbers, which will also result in a negative root. This is different from square roots, which are not real for negative numbers.

Learn how to evaluate cube roots of negative numbers with a detailed calculation. Understand the concept of cube roots and their application to negative numbers. Suitable for high school students in Grades 10-12.

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